With the WBC belt on the line, Brit Tyson Fury and American Deontay Wilder added another memorable contest to the division's golden run, which ended in a controversial draw. Both Barry and Parker were in attendance at Los Angeles' Staples Centre to witness the drama first-hand.
Barry stressed that it's now over to Parker to prove he belongs in the upper echelon of the division with an emphatic win over Alexander Flores in Christchurch later this month.
"Tyson Fury really lifted the bar last night," he said. "Joseph Parker really needs a good performance if he's to be thought of in the same breath as these elite guys - the Wilders the Tyson Furys, the Anthony Joshuas, the Dillian Whytes.
"The top guys in the division are all standing out at the moment and it's very important for Joe that he not only wins on the 15th, but he wins well."
The Kiwi-Samoan is coming off two consecutive losses, albeit against opponents of the highest calibre in Anthony Joshua and Dillian Whyte.
Facing the relatively unheralded Flores brings with it the added expectation of not just victory, but victory in comprehensive fashion.
Anything less than a knock-out would likely be considered a disappointment and severely hinder his chances of stepping back up to face the cream of the division, and, in doing so, get his title aspirations back on track.
Barry was hugely impressed by the underdone Fury, and shared the popular opinion that the 'Gypsy King' deserved to be awarded the decision win.
"Against all odds, he produced the performance of a lifetime, outboxing – as it looked to me – Deontay Wilder.
"Sure, [Fury] hit the canvas twice during the figh,t but most people there in the arena and most of the boxing experts around the world thought that he'd done enough on the scorecards to win.
He believes a rematch between the two is almost inevitable, and woul;d likely take place in the first quarter of 2019.
"Both of them probably can't get that money fighting anyone else other than Anthony Joshua, so there's a good chance we'll see a rematch taking place."
That rematch may ultimately become mandatory if Fury's promoter Frank Warren and the British Boxing Board Board of Control have their way.
They've confirmed an appeal will be made to the WBC for a review of the judge's decision.
"I've spoken to Charlie Giles, president of the British Boxing Board of Control, and they, along with us, will be writing to the WBC, asking that they look at what's gone on there and to order the rematch," Warren said.
"I genuinely feel sorry for Tyson - he's been robbed, and it wasn't right."